The microwave oven is a ubiquitous feature in modern society. However, its limitations are well known. These include, for example uneven heating and slow absorption of heat, especially for defrosting. In fact, ordinary microwave ovens, when used for defrosting and even heating, result in foods in which the outside is generally warm or even partly cooked before the interior is defrosted.
A number of papers have been published in which a theoretical analysis of the problem of warming of a cryogenic sample has been carried out. Because of the difficulties of such analysis, such analysis has only been carried out on regular shapes, such as spherical, and ellipsoidal shapes. Experimental attempts have apparently been made on kidney sized specimens, but results of these experiments do not indicate that a viable solution for defrosting kidneys is available.
Moreover, there does not appear to be a solution for defrosting other organs or foods of more arbitrary shapes.
Prior art publications include:    S. Evans, Electromagnetic Rewarming: The effect of CPA concentration and radio source frequency on uniformity and efficiency of heating, Cryobiology 40 (2000) 126-138.    S. Evans, et al., Design of a UHF applicator for rewarming of cryopreserved biomaterials, IEEE Trans. Biomed. Eng. 39 (1992) 217-225.    M. P. Robinson, et al., Rapid electromagnetic warming of cells and tissues, IEEE Trans. Biomed. Eng. 46 (1999) 1413-1425.    M. P. Robinson, et al., Electromagnetic re-warming of cryopreserved tissues: effect of choice of cryoprotectant and sample shape on uniformity of heating, Phys. Med. Biol. 47 (2002) 2311-2325.    M. C. Wusteman, Martin et al., Vitrification of large tissues with dielectric warming: biological problems and some approaches to their solution, Cryobiology 48 (2004) 179-189.
A paper entitled “Control of Thermal Runaway and Uniformity of Heating in the Electromagnetic Warming of a Cryopreserved Kidney Phantom” by J. D. J. Penfold, et al., in Cryobiology 30, 493-508 (1993) describes a theoretical analysis and experimental results. While some experiments were apparently made with a kidney sized phantom, the main reported results are with a uniform spherical object.
As reported a cavity was fed with electromagnetic energy at 434 MHz from three orthogonal directions (x, y, z). The x and y feeds were provided from a same generator and a phase change was introduced so that the field was circularly polarized. The frequency was varied in steps of 32 kHz (apparently up to about 350 kHz maximum) to match the input impedance as it changed with increasing temperature.
U.S. Pat. No. 6,249,710 describes using a zip code to estimate elevation and modify microwave oven operation.
All of the above articles and publications are incorporated herein by reference.